It is known that a certain slot machine has a 5% chance of winning. Suppose that a person plays the machine 500 times.
(a) Explain why this probability can be determined using the binomial distribution. However, do NOT attempt to compute this probability using the binomial distribution.
(b) Use the normal approximation to the binomial distribution to determine the probability that the person wins 30 times out of 500.
(c) Use the normal approximation to the binomial distribution to determine the probability that the person wins at least 30 times out of 500.